Question

lk goes through the center of the wheel pictured. find the diameter of the wheel. use the intersecting chords theorem to write the equation. the diameter of the wheel is 23 cm 28 cm 32 cm

Explanation:

Step1: Recall intersecting chords theorem

If two chords \(AB\) and \(CD\) intersect at a point \(M\) inside a circle, then \(AM\times BM=CM\times DM\). Here, one chord has segments \(16\) cm and \(7\) cm, and the other has segments \(4\) cm and \(x\) cm. So the equation is \(16\times7 = 4\times x\).

Step2: Solve for \(x\)

\[

$$\begin{align*} 16\times7&=4\times x\\ 112&=4x\\ x&=\frac{112}{4}=28 \end{align*}$$

\]
The diameter of the circle is the sum of the two - segment lengths of the chord that passes through the center. The chord passing through the center has segments \(4\) cm and \(28\) cm, so the diameter \(d=4 + 28=32\) cm.

Answer:

32 cm